diff --git a/.gitattributes b/.gitattributes
index 05402fda571..cc88b62c9a1 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -2293,12 +2293,27 @@ Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/collapse.sxi
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/collapse0.sxi -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/collapse1.sxi -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/edge_collapse.tex -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse1.eps -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse1.pdf -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse1.png -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse2.eps -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse2.pdf -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse2.png -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse3.eps -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse3.pdf -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse3.png -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse4.eps -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse4.pdf -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse4.png -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse0.eps -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse0.pdf -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse0.png -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse1.eps -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse1.pdf -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/collapse1.png -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/general_collapse.eps -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/general_collapse.pdf -text
+Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/general_collapse.png -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/intro.tex -text
Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/main.tex -text
Surface_mesh_simplification/examples/Surface_mesh_simplification/cgal_test -text
diff --git a/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/EdgeCollapsableMesh.tex b/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/EdgeCollapsableMesh.tex
index 6fccda60023..43339fe3838 100644
--- a/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/EdgeCollapsableMesh.tex
+++ b/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/EdgeCollapsableMesh.tex
@@ -63,10 +63,12 @@ Then, after the collapse of \ccc{(v0v1,v1v0)} the following holds:
\begin{itemize}
\item The edge \ccc{e} is no longer in \ccc{mesh}.
-\item One of $\{$\ccc{v0,v1}$\}$ is no longer in \ccc{mesh} while the other is kept. Let \ccc{vr} be the one removed and \ccc{vk} be the one kept.
+\item One of $\{$\ccc{v0,v1}$\}$ is no longer in \ccc{mesh} while the other remains.
+\footnote{Even though it would appear that v0 can always be the vertex being removed, there is one exception case (illustrated in Figure 4) when v1 must be the vertex removed.}
+Let \ccc{vm} be the removed vertex and \ccc{vk} be the remaining vertex.
\item If \ccc{e} was a border edge, that is \ccc{get(is_border, e, mesh) == true}, then \ccc{next_edge(ep) == en}, and \ccc{prev_edge(en) == ep}.
\item If \ccc{e} was not a border edge, that is \ccc{get(is_border, e, mesh) == false}, then \ccc{ep} and \ccc{epo} are no longer in \ccc{mesh} while \ccc{en} and \ccc{eno} are kept in \ccc{mesh}.
-\item For all edges \ccc{ie} in \ccc{in_edges(vr,mesh)}, \ccc{target(ie,mesh) == vk} and \ccc{source(opposite_edge(ie),mesh) == vk}.
+\item For all edges \ccc{ie} in \ccc{in_edges(vm,mesh)}, \ccc{target(ie,mesh) == vk} and \ccc{source(opposite_edge(ie),mesh) == vk}.
\item No other incidence information has changed in \ccc{mesh}.
\end{itemize}
@@ -87,27 +89,10 @@ The function returns vertex \ccc{vk}.
\end{ccHtmlOnly}
-\caption{General edge collapse case: The horizontal dotted line is the collapsing edge. Two of its incident edges are removed (dashed lines). The red and magenta lines are the edges which get re-linked to $u$. Blue and cyan lines are the edges left untouched because they are already linked to $u$.}
+\caption{General case. The following mesh elements are removed: triangles ($v0,v1,vL$) and ($v1,v0,vR$), edges $(e,e')$, $(ep,epo)$ and $(ep',epo')$, and vertex $v0$.}
\end{figure}
-\begin{figure}[htbp]
-\begin{ccTexOnly}
-\begin{center}
-\includegraphics[width=17cm]{Surface_mesh_simplification_ref/fig/border_collapse1} % omit suffix .eps to support PS and PDF
-\end{center}
-\end{ccTexOnly}
-\begin{ccHtmlOnly}
-
-
-
-
-
-
-
-\end{ccHtmlOnly}
-\caption{The case when the collapsing edge is a border. Only one of its incident edges (dashed line) is removed.}
-\end{figure}
\begin{figure}[htbp]
\begin{ccTexOnly}
@@ -124,7 +109,7 @@ The function returns vertex \ccc{vk}.
\end{ccHtmlOnly}
-\caption{The case when the collapsing edge is not itself a border, but is incident upon a border edge that is removed.}
+\caption{When the collapsing edge is not itself a border, but is incident upon a border edge that is removed, the operation is the same as in the general case.}
\end{figure}
\begin{figure}[htbp]
@@ -142,7 +127,25 @@ The function returns vertex \ccc{vk}.
\end{ccHtmlOnly}
-\caption{The case when the collapsing edge is not itself a border, but is incident upon a border edge that is {\em not} removed.}
+\caption{When the collapsing edge is not itself a border, but is incident upon a border edge that is {\em not} removed, the operation is still the same as in the general case.}
+\end{figure}
+
+\begin{figure}[htbp]
+\begin{ccTexOnly}
+\begin{center}
+\includegraphics[width=17cm]{Surface_mesh_simplification_ref/fig/border_collapse1} % omit suffix .eps to support PS and PDF
+\end{center}
+\end{ccTexOnly}
+\begin{ccHtmlOnly}
+
+
+
+
+
+
+
+\end{ccHtmlOnly}
+\caption{When the collapsing edge is itself a border, only 1 triangle is removed. Thus, even if $(ep',epo')$ exists, it's not removed.}
\end{figure}
\begin{figure}[htbp]
@@ -160,30 +163,9 @@ The function returns vertex \ccc{vk}.
\end{ccHtmlOnly}
-\caption{The single exceptional case when the vertex w instead of v is removed.}
+\caption{This figures illustrates the single exceptional case when vertex v0 cannot be removed, so v1 is removed instead (which also is a border case hence only 1 triangle is removed).}
\end{figure}
-
-\begin{figure}[htbp]
-\begin{ccTexOnly}
-\begin{center}
-\includegraphics[width=17cm]{Surface_mesh_simplification_ref/fig/collapse1} % omit suffix .eps to support PS and PDF
-\end{center}
-\end{ccTexOnly}
-\begin{ccHtmlOnly}
-
-
-
-
-
-
-
-\end{ccHtmlOnly}
-\caption{Detailed diagram of the collapse operation in a border case.}
-\end{figure}
-%% figures of simplified surfaces
-
-
\ccHasModels
\ccRefIdfierPage{CGAL::Polyhedron_3} with only triangular faces, via external adaptation.
diff --git a/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse1.eps b/Surface_mesh_simplification/doc_tex/Surface_mesh_simplification_ref/fig/border_collapse1.eps
new file mode 100644
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